### Problem 3–106A 170-kg granite rock (density \( \rho = 2700 \, \text{kg/m}^3 \)) is dropped into a lake. A man dives in and tries to lift the rock. Determine how much force the man needs to apply to lift it from the bottom of the lake. Do you think he can do it?### Solution Explanation:1. **Determine the volume of the rock**: - Use the formula for density: \( \text{density} = \frac{\text{mass}}{\text{volume}} \). - Rearranging gives: \( \text{volume} = \frac{\text{mass}}{\text{density}} \).2. **Calculate the buoyant force**: - Use Archimedes' principle: The buoyant force is equal to the weight of the displaced water. - Buoyant force = \(\text{volume of rock} \times \text{density of water} \times \text{gravity}\).3. **Calculate the weight of the rock in air**: - Weight = \( \text{mass} \times \text{gravity} \).4. **Determine the net force needed to lift**: - Net force = \(\text{weight of rock} - \text{buoyant force}\).This problem can explore concepts of buoyancy, density, and the physical limits of human strength.

Given data: Mass of granite (m)=170 kg density of granite (ρ)=2700 kg/m3

3-106 A 170-kg granite rock (p = 2700 kg/m³) is dropped into a lake. A man dives in and tries to lift the rock. Deter- mine how much force the man needs to apply to lift it from the bottom of the lake. Do you think he can do it?

3-106 A 170-kg granite rock (p = 2700 kg/m³) is dropped into a lake. A man dives in and tries to lift the rock. Deter- mine how much force the man needs to apply to lift it from the bottom of the lake. Do you think he can do it?

Structural Analysis

6th Edition

ISBN:9781337630931

Author:KASSIMALI, Aslam.

Publisher:KASSIMALI, Aslam.

Chapter2: Loads On Structures

Section: Chapter Questions

Problem 1P

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Question

### Problem 3–106

A 170-kg granite rock (density \( \rho = 2700 \, \text{kg/m}^3 \)) is dropped into a lake. A man dives in and tries to lift the rock. Determine how much force the man needs to apply to lift it from the bottom of the lake. Do you think he can do it?

### Solution Explanation:

1. **Determine the volume of the rock**:
- Use the formula for density: \( \text{density} = \frac{\text{mass}}{\text{volume}} \).
- Rearranging gives: \( \text{volume} = \frac{\text{mass}}{\text{density}} \).

2. **Calculate the buoyant force**:
- Use Archimedes' principle: The buoyant force is equal to the weight of the displaced water.
- Buoyant force = \(\text{volume of rock} \times \text{density of water} \times \text{gravity}\).

3. **Calculate the weight of the rock in air**:
- Weight = \( \text{mass} \times \text{gravity} \).

4. **Determine the net force needed to lift**:
- Net force = \(\text{weight of rock} - \text{buoyant force}\).

This problem can explore concepts of buoyancy, density, and the physical limits of human strength.

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